LMFDB - Embedded newform 1470.2.m.a.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.2
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.a.1273.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-0.707107 + 2.12132i) q^{10} +4.79271 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-4.37849 - 4.37849i) q^{13} +(0.707107 - 2.12132i) q^{15} -1.00000 q^{16} +(1.38896 - 1.38896i) q^{17} +(0.707107 - 0.707107i) q^{18} +3.41421 q^{19} +(2.00000 - 1.00000i) q^{20} +(-3.38896 - 3.38896i) q^{22} +(-3.00000 + 3.00000i) q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +6.19212i q^{26} +(-0.707107 + 0.707107i) q^{27} -1.42901i q^{29} +(-2.00000 + 1.00000i) q^{30} -0.813631i q^{31} +(0.707107 + 0.707107i) q^{32} +(3.38896 + 3.38896i) q^{33} -1.96428 q^{34} -1.00000 q^{36} +(-6.18166 - 6.18166i) q^{37} +(-2.41421 - 2.41421i) q^{38} -6.19212i q^{39} +(-2.12132 - 0.707107i) q^{40} -1.92856i q^{41} +(5.83889 - 5.83889i) q^{43} +4.79271i q^{44} +(2.00000 - 1.00000i) q^{45} +4.24264 q^{46} +(6.59588 - 6.59588i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(4.94975 - 0.707107i) q^{50} +1.96428 q^{51} +(4.37849 - 4.37849i) q^{52} +(-7.91376 + 7.91376i) q^{53} +1.00000 q^{54} +(-4.79271 - 9.58541i) q^{55} +(2.41421 + 2.41421i) q^{57} +(-1.01046 + 1.01046i) q^{58} -5.36370 q^{59} +(2.12132 + 0.707107i) q^{60} -9.58541i q^{61} +(-0.575324 + 0.575324i) q^{62} -1.00000i q^{64} +(-4.37849 + 13.1355i) q^{65} -4.79271i q^{66} +(-6.36803 - 6.36803i) q^{67} +(1.38896 + 1.38896i) q^{68} -4.24264 q^{69} +14.9700 q^{71} +(0.707107 + 0.707107i) q^{72} +(-4.81363 - 4.81363i) q^{73} +8.74219i q^{74} +(-4.94975 + 0.707107i) q^{75} +3.41421i q^{76} +(-4.37849 + 4.37849i) q^{78} -1.92856i q^{79} +(1.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(-1.36370 + 1.36370i) q^{82} +(-2.51434 - 2.51434i) q^{83} +(-4.16687 - 1.38896i) q^{85} -8.25744 q^{86} +(1.01046 - 1.01046i) q^{87} +(3.38896 - 3.38896i) q^{88} -9.97908 q^{89} +(-2.12132 - 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(0.575324 - 0.575324i) q^{93} -9.32798 q^{94} +(-3.41421 - 6.82843i) q^{95} +1.00000i q^{96} +(11.2275 - 11.2275i) q^{97} +4.79271i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5}+O(q^{10}) $ 8 * q - 8 * q^5	$ 8 q - 8 q^{5} - 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 8 q^{24} - 24 q^{25} - 16 q^{30} + 8 q^{33} - 8 q^{36} + 8 q^{37} - 8 q^{38} + 32 q^{43} + 16 q^{45} - 16 q^{47} + 8 q^{52} - 32 q^{53} + 8 q^{54} + 8 q^{57} - 16 q^{58} - 16 q^{59} - 8 q^{62} - 8 q^{65} - 16 q^{67} - 8 q^{68} + 32 q^{71} - 16 q^{73} - 8 q^{78} + 8 q^{80} - 8 q^{81} + 16 q^{82} + 24 q^{85} - 32 q^{86} + 16 q^{87} + 8 q^{88} - 64 q^{89} - 24 q^{92} + 8 q^{93} - 32 q^{94} - 16 q^{95} - 32 q^{97}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 8 * q^24 - 24 * q^25 - 16 * q^30 + 8 * q^33 - 8 * q^36 + 8 * q^37 - 8 * q^38 + 32 * q^43 + 16 * q^45 - 16 * q^47 + 8 * q^52 - 32 * q^53 + 8 * q^54 + 8 * q^57 - 16 * q^58 - 16 * q^59 - 8 * q^62 - 8 * q^65 - 16 * q^67 - 8 * q^68 + 32 * q^71 - 16 * q^73 - 8 * q^78 + 8 * q^80 - 8 * q^81 + 16 * q^82 + 24 * q^85 - 32 * q^86 + 16 * q^87 + 8 * q^88 - 64 * q^89 - 24 * q^92 + 8 * q^93 - 32 * q^94 - 16 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−0.707107	+	2.12132i	−0.223607	+	0.670820i
$11$	4.79271			1.44506			0.722528	−	0.691342i	$-0.242980\pi$
$11$	4.79271			1.44506			0.722528	+	0.691342i	$0.242980\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−4.37849	−	4.37849i	−1.21438	−	1.21438i	−0.969573	−	0.244802i	$-0.921277\pi$
$13$	−4.37849	−	4.37849i	−1.21438	−	1.21438i	−0.244802	−	0.969573i	$-0.578723\pi$
$14$		0			0
$15$	0.707107	−	2.12132i	0.182574	−	0.547723i
$16$	−1.00000			−0.250000
$17$	1.38896	−	1.38896i	0.336871	−	0.336871i	−0.518317	−	0.855188i	$-0.673441\pi$
$17$	1.38896	−	1.38896i	0.336871	−	0.336871i	0.855188	+	0.518317i	$0.173441\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	3.41421			0.783274			0.391637	−	0.920120i	$-0.371909\pi$
$19$	3.41421			0.783274			0.391637	+	0.920120i	$0.371909\pi$
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$		0			0
$22$	−3.38896	−	3.38896i	−0.722528	−	0.722528i
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	−0.946943	−	0.321400i	$-0.895847\pi$
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	0.321400	+	0.946943i	$0.395847\pi$
$24$	1.00000			0.204124
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$			6.19212i			1.21438i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	1.42901i		−	0.265360i	−0.991159	−	0.132680i	$-0.957642\pi$
$29$		−	1.42901i		−	0.265360i	0.991159	−	0.132680i	$-0.0423583\pi$
$30$	−2.00000	+	1.00000i	−0.365148	+	0.182574i
$31$		−	0.813631i		−	0.146132i	−0.997327	−	0.0730662i	$-0.976722\pi$
$31$		−	0.813631i		−	0.146132i	0.997327	−	0.0730662i	$-0.0232784\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.38896	+	3.38896i	0.589941	+	0.589941i
$34$	−1.96428			−0.336871
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−6.18166	−	6.18166i	−1.01626	−	1.01626i	−0.999866	−	0.0163933i	$-0.994782\pi$
$37$	−6.18166	−	6.18166i	−1.01626	−	1.01626i	−0.0163933	−	0.999866i	$-0.505218\pi$
$38$	−2.41421	−	2.41421i	−0.391637	−	0.391637i
$39$		−	6.19212i		−	0.991533i
$40$	−2.12132	−	0.707107i	−0.335410	−	0.111803i
$41$		−	1.92856i		−	0.301190i	−0.988596	−	0.150595i	$-0.951881\pi$
$41$		−	1.92856i		−	0.301190i	0.988596	−	0.150595i	$-0.0481190\pi$
$42$		0			0
$43$	5.83889	−	5.83889i	0.890422	−	0.890422i	−0.104140	−	0.994563i	$-0.533209\pi$
$43$	5.83889	−	5.83889i	0.890422	−	0.890422i	0.994563	+	0.104140i	$0.0332091\pi$
$44$			4.79271i			0.722528i
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$	4.24264			0.625543
$47$	6.59588	−	6.59588i	0.962107	−	0.962107i	−0.0372006	−	0.999308i	$-0.511844\pi$
$47$	6.59588	−	6.59588i	0.962107	−	0.962107i	0.999308	+	0.0372006i	$0.0118440\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		0			0
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$	1.96428			0.275054
$52$	4.37849	−	4.37849i	0.607188	−	0.607188i
$53$	−7.91376	+	7.91376i	−1.08704	+	1.08704i	−0.0912069	+	0.995832i	$0.529072\pi$
$53$	−7.91376	+	7.91376i	−1.08704	+	1.08704i	−0.995832	+	0.0912069i	$0.970928\pi$
$54$	1.00000			0.136083
$55$	−4.79271	−	9.58541i	−0.646248	−	1.29250i
$56$		0			0
$57$	2.41421	+	2.41421i	0.319770	+	0.319770i
$58$	−1.01046	+	1.01046i	−0.132680	+	0.132680i
$59$	−5.36370			−0.698294			−0.349147	−	0.937068i	$-0.613529\pi$
$59$	−5.36370			−0.698294			−0.349147	+	0.937068i	$0.613529\pi$
$60$	2.12132	+	0.707107i	0.273861	+	0.0912871i
$61$		−	9.58541i		−	1.22729i	−0.789583	−	0.613643i	$-0.789703\pi$
$61$		−	9.58541i		−	1.22729i	0.789583	−	0.613643i	$-0.210297\pi$
$62$	−0.575324	+	0.575324i	−0.0730662	+	0.0730662i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.37849	+	13.1355i	−0.543085	+	1.62926i
$66$		−	4.79271i		−	0.589941i
$67$	−6.36803	−	6.36803i	−0.777979	−	0.777979i	0.201508	−	0.979487i	$-0.435416\pi$
$67$	−6.36803	−	6.36803i	−0.777979	−	0.777979i	−0.979487	+	0.201508i	$0.935416\pi$
$68$	1.38896	+	1.38896i	0.168436	+	0.168436i
$69$	−4.24264			−0.510754
$70$		0			0
$71$	14.9700			1.77662			0.888308	−	0.459248i	$-0.151881\pi$
$71$	14.9700			1.77662			0.888308	+	0.459248i	$0.151881\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−4.81363	−	4.81363i	−0.563393	−	0.563393i	0.366877	−	0.930270i	$-0.380427\pi$
$73$	−4.81363	−	4.81363i	−0.563393	−	0.563393i	−0.930270	+	0.366877i	$0.880427\pi$
$74$			8.74219i			1.01626i
$75$	−4.94975	+	0.707107i	−0.571548	+	0.0816497i
$76$			3.41421i			0.391637i
$77$		0			0
$78$	−4.37849	+	4.37849i	−0.495767	+	0.495767i
$79$		−	1.92856i		−	0.216980i	−0.994098	−	0.108490i	$-0.965398\pi$
$79$		−	1.92856i		−	0.216980i	0.994098	−	0.108490i	$-0.0346015\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	−1.00000			−0.111111
$82$	−1.36370	+	1.36370i	−0.150595	+	0.150595i
$83$	−2.51434	−	2.51434i	−0.275985	−	0.275985i	0.555519	−	0.831504i	$-0.312520\pi$
$83$	−2.51434	−	2.51434i	−0.275985	−	0.275985i	−0.831504	+	0.555519i	$0.812520\pi$
$84$		0			0
$85$	−4.16687	−	1.38896i	−0.451960	−	0.150653i
$86$	−8.25744			−0.890422
$87$	1.01046	−	1.01046i	0.108333	−	0.108333i
$88$	3.38896	−	3.38896i	0.361264	−	0.361264i
$89$	−9.97908			−1.05778			−0.528890	−	0.848690i	$-0.677392\pi$
$89$	−9.97908			−1.05778			−0.528890	+	0.848690i	$0.677392\pi$
$90$	−2.12132	−	0.707107i	−0.223607	−	0.0745356i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$	0.575324	−	0.575324i	0.0596583	−	0.0596583i
$94$	−9.32798			−0.962107
$95$	−3.41421	−	6.82843i	−0.350291	−	0.700582i
$96$			1.00000i			0.102062i
$97$	11.2275	−	11.2275i	1.13998	−	1.13998i	0.151523	−	0.988454i	$-0.451582\pi$
$97$	11.2275	−	11.2275i	1.13998	−	1.13998i	0.988454	−	0.151523i	$-0.0484178\pi$
$98$		0			0
$99$			4.79271i			0.481685i
$100$	−4.00000	−	3.00000i	−0.400000	−	0.300000i
$101$		−	12.9700i		−	1.29057i	−0.763943	−	0.645283i	$-0.776739\pi$
$101$		−	12.9700i		−	1.29057i	0.763943	−	0.645283i	$-0.223261\pi$
$102$	−1.38896	−	1.38896i	−0.137527	−	0.137527i
$103$	8.82843	+	8.82843i	0.869891	+	0.869891i	0.992460	−	0.122569i	$-0.0391133\pi$
$103$	8.82843	+	8.82843i	0.869891	+	0.869891i	−0.122569	+	0.992460i	$0.539113\pi$
$104$	−6.19212			−0.607188
$105$		0			0
$106$	11.1918			1.08704
$107$	9.62113	+	9.62113i	0.930110	+	0.930110i	0.997712	−	0.0676023i	$-0.0215349\pi$
$107$	9.62113	+	9.62113i	0.930110	+	0.930110i	−0.0676023	+	0.997712i	$0.521535\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	14.4348i		−	1.38260i	−0.722568	−	0.691300i	$-0.757038\pi$
$109$		−	14.4348i		−	1.38260i	0.722568	−	0.691300i	$-0.242962\pi$
$110$	−3.38896	+	10.1669i	−0.323124	+	0.969373i
$111$		−	8.74219i		−	0.829772i
$112$		0			0
$113$	−0.0209247	+	0.0209247i	−0.00196843	+	0.00196843i	−0.708090	−	0.706122i	$-0.750443\pi$
$113$	−0.0209247	+	0.0209247i	−0.00196843	+	0.00196843i	0.706122	+	0.708090i	$0.250443\pi$
$114$		−	3.41421i		−	0.319770i
$115$	9.00000	+	3.00000i	0.839254	+	0.279751i
$116$	1.42901			0.132680
$117$	4.37849	−	4.37849i	0.404792	−	0.404792i
$118$	3.79271	+	3.79271i	0.349147	+	0.349147i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	11.9700			1.08818
$122$	−6.77791	+	6.77791i	−0.613643	+	0.613643i
$123$	1.36370	−	1.36370i	0.122960	−	0.122960i
$124$	0.813631			0.0730662
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	−8.97003	−	8.97003i	−0.795962	−	0.795962i	0.186494	−	0.982456i	$-0.440287\pi$
$127$	−8.97003	−	8.97003i	−0.795962	−	0.795962i	−0.982456	+	0.186494i	$0.940287\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	8.25744			0.727027
$130$	12.3842	−	6.19212i	1.08617	−	0.543085i
$131$			0.293157i			0.0256133i	0.999918	+	0.0128066i	$0.00407659\pi$
$131$			0.293157i			0.0256133i	−0.999918	+	0.0128066i	$0.995923\pi$
$132$	−3.38896	+	3.38896i	−0.294971	+	0.294971i
$133$		0			0
$134$			9.00575i			0.777979i
$135$	2.12132	+	0.707107i	0.182574	+	0.0608581i
$136$		−	1.96428i		−	0.168436i
$137$	9.17733	+	9.17733i	0.784072	+	0.784072i	0.980515	−	0.196443i	$-0.0629391\pi$
$137$	9.17733	+	9.17733i	0.784072	+	0.784072i	−0.196443	+	0.980515i	$0.562939\pi$
$138$	3.00000	+	3.00000i	0.255377	+	0.255377i
$139$	−18.6983			−1.58597			−0.792986	−	0.609240i	$-0.791475\pi$
$139$	−18.6983			−1.58597			−0.792986	+	0.609240i	$0.791475\pi$
$140$		0			0
$141$	9.32798			0.785557
$142$	−10.5854	−	10.5854i	−0.888308	−	0.888308i
$143$	−20.9848	−	20.9848i	−1.75484	−	1.75484i
$144$		−	1.00000i		−	0.0833333i
$145$	−2.85802	+	1.42901i	−0.237346	+	0.118673i
$146$			6.80750i			0.563393i
$147$		0			0
$148$	6.18166	−	6.18166i	0.508129	−	0.508129i
$149$		−	1.86452i		−	0.152748i	−0.997079	−	0.0763738i	$-0.975666\pi$
$149$		−	1.86452i		−	0.152748i	0.997079	−	0.0763738i	$-0.0243342\pi$
$150$	4.00000	+	3.00000i	0.326599	+	0.244949i
$151$	8.15027			0.663260			0.331630	−	0.943410i	$-0.392401\pi$
$151$	8.15027			0.663260			0.331630	+	0.943410i	$0.392401\pi$
$152$	2.41421	−	2.41421i	0.195819	−	0.195819i
$153$	1.38896	+	1.38896i	0.112290	+	0.112290i
$154$		0			0
$155$	−1.62726	+	0.813631i	−0.130705	+	0.0653524i
$156$	6.19212			0.495767
$157$	−13.0711	+	13.0711i	−1.04318	+	1.04318i	−0.0441603	+	0.999024i	$0.514061\pi$
$157$	−13.0711	+	13.0711i	−1.04318	+	1.04318i	−0.999024	+	0.0441603i	$0.985939\pi$
$158$	−1.36370	+	1.36370i	−0.108490	+	0.108490i
$159$	−11.1918			−0.887564
$160$	0.707107	−	2.12132i	0.0559017	−	0.167705i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	3.48909	−	3.48909i	0.273286	−	0.273286i	−0.557135	−	0.830422i	$-0.688100\pi$
$163$	3.48909	−	3.48909i	0.273286	−	0.273286i	0.830422	+	0.557135i	$0.188100\pi$
$164$	1.92856			0.150595
$165$	3.38896	−	10.1669i	0.263830	−	0.791489i
$166$			3.55582i			0.275985i
$167$	12.0754	−	12.0754i	0.934423	−	0.934423i	−0.0635557	−	0.997978i	$-0.520244\pi$
$167$	12.0754	−	12.0754i	0.934423	−	0.934423i	0.997978	+	0.0635557i	$0.0202440\pi$
$168$		0			0
$169$			25.3424i			1.94942i
$170$	1.96428	+	3.92856i	0.150653	+	0.301307i
$171$			3.41421i			0.261091i
$172$	5.83889	+	5.83889i	0.445211	+	0.445211i
$173$	−11.4638	−	11.4638i	−0.871579	−	0.871579i	0.121066	−	0.992644i	$-0.461369\pi$
$173$	−11.4638	−	11.4638i	−0.871579	−	0.871579i	−0.992644	+	0.121066i	$0.961369\pi$
$174$	−1.42901			−0.108333
$175$		0			0
$176$	−4.79271			−0.361264
$177$	−3.79271	−	3.79271i	−0.285077	−	0.285077i
$178$	7.05627	+	7.05627i	0.528890	+	0.528890i
$179$			15.9845i			1.19473i	0.801968	+	0.597367i	$0.203786\pi$
$179$			15.9845i			1.19473i	−0.801968	+	0.597367i	$0.796214\pi$
$180$	1.00000	+	2.00000i	0.0745356	+	0.149071i
$181$			10.3128i			0.766545i	0.923635	+	0.383272i	$0.125203\pi$
$181$			10.3128i			0.766545i	−0.923635	+	0.383272i	$0.874797\pi$
$182$		0			0
$183$	6.77791	−	6.77791i	0.501038	−	0.501038i
$184$			4.24264i			0.312772i
$185$	−6.18166	+	18.5450i	−0.454485	+	1.36345i
$186$	−0.813631			−0.0596583
$187$	6.65685	−	6.65685i	0.486797	−	0.486797i
$188$	6.59588	+	6.59588i	0.481054	+	0.481054i
$189$		0			0
$190$	−2.41421	+	7.24264i	−0.175145	+	0.525436i
$191$	14.5143			1.05022			0.525111	−	0.851034i	$-0.324024\pi$
$191$	14.5143			1.05022			0.525111	+	0.851034i	$0.324024\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−5.19212	+	5.19212i	−0.373737	+	0.373737i	−0.868836	−	0.495099i	$-0.835132\pi$
$193$	−5.19212	+	5.19212i	−0.373737	+	0.373737i	0.495099	+	0.868836i	$0.335132\pi$
$194$	−15.8780			−1.13998
$195$	−12.3842	+	6.19212i	−0.886854	+	0.443427i
$196$		0			0
$197$	−11.7775	−	11.7775i	−0.839115	−	0.839115i	0.149628	−	0.988742i	$-0.452192\pi$
$197$	−11.7775	−	11.7775i	−0.839115	−	0.839115i	−0.988742	+	0.149628i	$0.952192\pi$
$198$	3.38896	−	3.38896i	0.240843	−	0.240843i
$199$	2.12809			0.150856			0.0754280	−	0.997151i	$-0.475968\pi$
$199$	2.12809			0.150856			0.0754280	+	0.997151i	$0.475968\pi$
$200$	0.707107	+	4.94975i	0.0500000	+	0.350000i
$201$		−	9.00575i		−	0.635217i
$202$	−9.17120	+	9.17120i	−0.645283	+	0.645283i
$203$		0			0
$204$			1.96428i			0.137527i
$205$	−3.85712	+	1.92856i	−0.269393	+	0.134696i
$206$		−	12.4853i		−	0.869891i
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$	4.37849	+	4.37849i	0.303594	+	0.303594i
$209$	16.3633			1.13187
$210$		0			0
$211$	−15.6655			−1.07846			−0.539229	−	0.842159i	$-0.681284\pi$
$211$	−15.6655			−1.07846			−0.539229	+	0.842159i	$0.681284\pi$
$212$	−7.91376	−	7.91376i	−0.543519	−	0.543519i
$213$	10.5854	+	10.5854i	0.725301	+	0.725301i
$214$		−	13.6063i		−	0.930110i
$215$	−17.5167	−	5.83889i	−1.19463	−	0.398209i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−10.2069	+	10.2069i	−0.691300	+	0.691300i
$219$		−	6.80750i		−	0.460008i
$220$	9.58541	−	4.79271i	0.646248	−	0.323124i
$221$	−12.1631			−0.818176
$222$	−6.18166	+	6.18166i	−0.414886	+	0.414886i
$223$	−8.76311	−	8.76311i	−0.586822	−	0.586822i	0.349948	−	0.936769i	$-0.386199\pi$
$223$	−8.76311	−	8.76311i	−0.586822	−	0.586822i	−0.936769	+	0.349948i	$0.886199\pi$
$224$		0			0
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	0.0295921			0.00196843
$227$	−8.29316	+	8.29316i	−0.550436	+	0.550436i	−0.926567	−	0.376131i	$-0.877254\pi$
$227$	−8.29316	+	8.29316i	−0.550436	+	0.550436i	0.376131	+	0.926567i	$0.377254\pi$
$228$	−2.41421	+	2.41421i	−0.159885	+	0.159885i
$229$	19.1001			1.26217			0.631086	−	0.775713i	$-0.282609\pi$
$229$	19.1001			1.26217			0.631086	+	0.775713i	$0.282609\pi$
$230$	−4.24264	−	8.48528i	−0.279751	−	0.559503i
$231$		0			0
$232$	−1.01046	−	1.01046i	−0.0663401	−	0.0663401i
$233$	10.5358	−	10.5358i	0.690223	−	0.690223i	−0.272058	−	0.962281i	$-0.587704\pi$
$233$	10.5358	−	10.5358i	0.690223	−	0.690223i	0.962281	+	0.272058i	$0.0877042\pi$
$234$	−6.19212			−0.404792
$235$	−19.7876	−	6.59588i	−1.29080	−	0.430267i
$236$		−	5.36370i		−	0.349147i
$237$	1.36370	−	1.36370i	0.0885816	−	0.0885816i
$238$		0			0
$239$			8.69833i			0.562648i	0.959613	+	0.281324i	$0.0907736\pi$
$239$			8.69833i			0.562648i	−0.959613	+	0.281324i	$0.909226\pi$
$240$	−0.707107	+	2.12132i	−0.0456435	+	0.136931i
$241$			6.79218i			0.437523i	0.975778	+	0.218761i	$0.0702016\pi$
$241$			6.79218i			0.437523i	−0.975778	+	0.218761i	$0.929798\pi$
$242$	−8.46409	−	8.46409i	−0.544092	−	0.544092i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	9.58541			0.613643
$245$		0			0
$246$	−1.92856			−0.122960
$247$	−14.9491	−	14.9491i	−0.951189	−	0.951189i
$248$	−0.575324	−	0.575324i	−0.0365331	−	0.0365331i
$249$		−	3.55582i		−	0.225341i
$250$	−6.36396	−	9.19239i	−0.402492	−	0.581378i
$251$			9.34330i			0.589744i	0.955537	+	0.294872i	$0.0952770\pi$
$251$			9.34330i			0.589744i	−0.955537	+	0.294872i	$0.904723\pi$
$252$		0			0
$253$	−14.3781	+	14.3781i	−0.903945	+	0.903945i
$254$			12.6855i			0.795962i
$255$	−1.96428	−	3.92856i	−0.123008	−	0.246016i
$256$	1.00000			0.0625000
$257$	−3.67546	+	3.67546i	−0.229269	+	0.229269i	−0.812387	−	0.583118i	$-0.801832\pi$
$257$	−3.67546	+	3.67546i	−0.229269	+	0.229269i	0.583118	+	0.812387i	$0.301832\pi$
$258$	−5.83889	−	5.83889i	−0.363513	−	0.363513i
$259$		0			0
$260$	−13.1355	−	4.37849i	−0.814628	−	0.271543i
$261$	1.42901			0.0884535
$262$	0.207294	−	0.207294i	0.0128066	−	0.0128066i
$263$	−8.79846	+	8.79846i	−0.542536	+	0.542536i	−0.924272	−	0.381735i	$-0.875327\pi$
$263$	−8.79846	+	8.79846i	−0.542536	+	0.542536i	0.381735	+	0.924272i	$0.375327\pi$
$264$	4.79271			0.294971
$265$	23.7413	+	7.91376i	1.45842	+	0.486139i
$266$		0			0
$267$	−7.05627	−	7.05627i	−0.431837	−	0.431837i
$268$	6.36803	−	6.36803i	0.388989	−	0.388989i
$269$	19.8982			1.21322			0.606608	−	0.795001i	$-0.292530\pi$
$269$	19.8982			1.21322			0.606608	+	0.795001i	$0.292530\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$			19.6211i			1.19190i	0.803022	+	0.595949i	$0.203224\pi$
$271$			19.6211i			1.19190i	−0.803022	+	0.595949i	$0.796776\pi$
$272$	−1.38896	+	1.38896i	−0.0842178	+	0.0842178i
$273$		0			0
$274$		−	12.9787i		−	0.784072i
$275$	−14.3781	+	19.1708i	−0.867033	+	1.15604i
$276$		−	4.24264i		−	0.255377i
$277$	11.3175	+	11.3175i	0.680003	+	0.680003i	0.960001	−	0.279997i	$-0.0903336\pi$
$277$	11.3175	+	11.3175i	0.680003	+	0.680003i	−0.279997	+	0.960001i	$0.590334\pi$
$278$	13.2217	+	13.2217i	0.792986	+	0.792986i
$279$	0.813631			0.0487108
$280$		0			0
$281$	15.4844			0.923721			0.461860	−	0.886953i	$-0.347182\pi$
$281$	15.4844			0.923721			0.461860	+	0.886953i	$0.347182\pi$
$282$	−6.59588	−	6.59588i	−0.392779	−	0.392779i
$283$	−8.68645	−	8.68645i	−0.516356	−	0.516356i	0.400111	−	0.916467i	$-0.368972\pi$
$283$	−8.68645	−	8.68645i	−0.516356	−	0.516356i	−0.916467	+	0.400111i	$0.868972\pi$
$284$			14.9700i			0.888308i
$285$	2.41421	−	7.24264i	0.143006	−	0.429017i
$286$			29.6770i			1.75484i
$287$		0			0
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			13.1416i			0.773036i
$290$	3.03139	+	1.01046i	0.178009	+	0.0593364i
$291$	15.8780			0.930787
$292$	4.81363	−	4.81363i	0.281696	−	0.281696i
$293$	21.7981	+	21.7981i	1.27346	+	1.27346i	0.944261	+	0.329196i	$0.106778\pi$
$293$	21.7981	+	21.7981i	1.27346	+	1.27346i	0.329196	+	0.944261i	$0.393222\pi$
$294$		0			0
$295$	5.36370	+	10.7274i	0.312286	+	0.624573i
$296$	−8.74219			−0.508129
$297$	−3.38896	+	3.38896i	−0.196647	+	0.196647i
$298$	−1.31842	+	1.31842i	−0.0763738	+	0.0763738i
$299$	26.2710			1.51929
$300$	−0.707107	−	4.94975i	−0.0408248	−	0.285774i
$301$		0			0
$302$	−5.76311	−	5.76311i	−0.331630	−	0.331630i
$303$	9.17120	−	9.17120i	0.526872	−	0.526872i
$304$	−3.41421			−0.195819
$305$	−19.1708	+	9.58541i	−1.09772	+	0.548859i
$306$		−	1.96428i		−	0.112290i
$307$	−3.10013	+	3.10013i	−0.176934	+	0.176934i	−0.790018	−	0.613084i	$-0.789929\pi$
$307$	−3.10013	+	3.10013i	−0.176934	+	0.176934i	0.613084	+	0.790018i	$0.289929\pi$
$308$		0			0
$309$			12.4853i			0.710263i
$310$	1.72597	+	0.575324i	0.0980286	+	0.0326762i
$311$			26.7180i			1.51504i	0.652813	+	0.757519i	$0.273589\pi$
$311$			26.7180i			1.51504i	−0.652813	+	0.757519i	$0.726411\pi$
$312$	−4.37849	−	4.37849i	−0.247883	−	0.247883i
$313$	3.39329	+	3.39329i	0.191800	+	0.191800i	0.796473	−	0.604673i	$-0.206696\pi$
$313$	3.39329	+	3.39329i	0.191800	+	0.191800i	−0.604673	+	0.796473i	$0.706696\pi$
$314$	18.4853			1.04318
$315$		0			0
$316$	1.92856			0.108490
$317$	−19.3839	−	19.3839i	−1.08871	−	1.08871i	−0.995662	−	0.0930449i	$-0.970340\pi$
$317$	−19.3839	−	19.3839i	−1.08871	−	1.08871i	−0.0930449	−	0.995662i	$-0.529660\pi$
$318$	7.91376	+	7.91376i	0.443782	+	0.443782i
$319$		−	6.84882i		−	0.383460i
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$			13.6063i			0.759432i
$322$		0			0
$323$	4.74219	−	4.74219i	0.263862	−	0.263862i
$324$		−	1.00000i		−	0.0555556i
$325$	30.6494	−	4.37849i	1.70013	−	0.242875i
$326$	−4.93431			−0.273286
$327$	10.2069	−	10.2069i	0.564444	−	0.564444i
$328$	−1.36370	−	1.36370i	−0.0752976	−	0.0752976i
$329$		0			0
$330$	−9.58541	+	4.79271i	−0.527660	+	0.263830i
$331$	33.6770			1.85106			0.925529	−	0.378678i	$-0.123621\pi$
$331$	33.6770			1.85106			0.925529	+	0.378678i	$0.123621\pi$
$332$	2.51434	−	2.51434i	0.137993	−	0.137993i
$333$	6.18166	−	6.18166i	0.338753	−	0.338753i
$334$	−17.0772			−0.934423
$335$	−6.36803	+	19.1041i	−0.347923	+	1.04377i
$336$		0			0
$337$	6.12158	+	6.12158i	0.333464	+	0.333464i	0.853900	−	0.520436i	$-0.174231\pi$
$337$	6.12158	+	6.12158i	0.333464	+	0.333464i	−0.520436	+	0.853900i	$0.674231\pi$
$338$	17.9198	−	17.9198i	0.974708	−	0.974708i
$339$	−0.0295921			−0.00160722
$340$	1.38896	−	4.16687i	0.0753267	−	0.225980i
$341$		−	3.89949i		−	0.211169i
$342$	2.41421	−	2.41421i	0.130546	−	0.130546i
$343$		0			0
$344$		−	8.25744i		−	0.445211i
$345$	4.24264	+	8.48528i	0.228416	+	0.456832i
$346$			16.2123i			0.871579i
$347$	11.1622	+	11.1622i	0.599216	+	0.599216i	0.940104	−	0.340888i	$-0.110728\pi$
$347$	11.1622	+	11.1622i	0.599216	+	0.599216i	−0.340888	+	0.940104i	$0.610728\pi$
$348$	1.01046	+	1.01046i	0.0541665	+	0.0541665i
$349$	−4.58631			−0.245500			−0.122750	−	0.992438i	$-0.539171\pi$
$349$	−4.58631			−0.245500			−0.122750	+	0.992438i	$0.539171\pi$
$350$		0			0
$351$	6.19212			0.330511
$352$	3.38896	+	3.38896i	0.180632	+	0.180632i
$353$	10.6016	+	10.6016i	0.564268	+	0.564268i	0.930517	−	0.366249i	$-0.119358\pi$
$353$	10.6016	+	10.6016i	0.564268	+	0.564268i	−0.366249	+	0.930517i	$0.619358\pi$
$354$			5.36370i			0.285077i
$355$	−14.9700	−	29.9401i	−0.794527	−	1.58905i
$356$		−	9.97908i		−	0.528890i
$357$		0			0
$358$	11.3027	−	11.3027i	0.597367	−	0.597367i
$359$			25.4553i			1.34348i	0.740787	+	0.671740i	$0.234453\pi$
$359$			25.4553i			1.34348i	−0.740787	+	0.671740i	$0.765547\pi$
$360$	0.707107	−	2.12132i	0.0372678	−	0.111803i
$361$	−7.34315			−0.386481
$362$	7.29226	−	7.29226i	0.383272	−	0.383272i
$363$	8.46409	+	8.46409i	0.444250	+	0.444250i
$364$		0			0
$365$	−4.81363	+	14.4409i	−0.251957	+	0.755871i
$366$	−9.58541			−0.501038
$367$	3.27799	−	3.27799i	0.171110	−	0.171110i	−0.616357	−	0.787467i	$-0.711392\pi$
$367$	3.27799	−	3.27799i	0.171110	−	0.171110i	0.787467	+	0.616357i	$0.211392\pi$
$368$	3.00000	−	3.00000i	0.156386	−	0.156386i
$369$	1.92856			0.100397
$370$	17.4844	−	8.74219i	0.908970	−	0.454485i
$371$		0			0
$372$	0.575324	+	0.575324i	0.0298292	+	0.0298292i
$373$	16.9596	−	16.9596i	0.878133	−	0.878133i	−0.115208	−	0.993341i	$-0.536753\pi$
$373$	16.9596	−	16.9596i	0.878133	−	0.878133i	0.993341	+	0.115208i	$0.0367535\pi$
$374$	−9.41421			−0.486797
$375$	6.36396	+	9.19239i	0.328634	+	0.474693i
$376$		−	9.32798i		−	0.481054i
$377$	−6.25691	+	6.25691i	−0.322247	+	0.322247i
$378$		0			0
$379$		−	15.7788i		−	0.810503i	−0.914205	−	0.405252i	$-0.867184\pi$
$379$		−	15.7788i		−	0.810503i	0.914205	−	0.405252i	$-0.132816\pi$
$380$	6.82843	−	3.41421i	0.350291	−	0.175145i
$381$		−	12.6855i		−	0.649900i
$382$	−10.2632	−	10.2632i	−0.525111	−	0.525111i
$383$	7.68174	+	7.68174i	0.392519	+	0.392519i	0.875584	−	0.483066i	$-0.160477\pi$
$383$	7.68174	+	7.68174i	0.392519	+	0.392519i	−0.483066	+	0.875584i	$0.660477\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	7.34277			0.373737
$387$	5.83889	+	5.83889i	0.296807	+	0.296807i
$388$	11.2275	+	11.2275i	0.569988	+	0.569988i
$389$			11.0657i			0.561053i	0.959846	+	0.280526i	$0.0905090\pi$
$389$			11.0657i			0.561053i	−0.959846	+	0.280526i	$0.909491\pi$
$390$	13.1355	+	4.37849i	0.665141	+	0.221714i
$391$			8.33373i			0.421455i
$392$		0			0
$393$	−0.207294	+	0.207294i	−0.0104566	+	0.0104566i
$394$			16.6560i			0.839115i
$395$	−3.85712	+	1.92856i	−0.194073	+	0.0970363i
$396$	−4.79271			−0.240843
$397$	−2.24264	+	2.24264i	−0.112555	+	0.112555i	−0.761141	−	0.648586i	$-0.775361\pi$
$397$	−2.24264	+	2.24264i	−0.112555	+	0.112555i	0.648586	+	0.761141i	$0.275361\pi$
$398$	−1.50478	−	1.50478i	−0.0754280	−	0.0754280i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	30.3121			1.51371			0.756856	−	0.653582i	$-0.226734\pi$
$401$	30.3121			1.51371			0.756856	+	0.653582i	$0.226734\pi$
$402$	−6.36803	+	6.36803i	−0.317608	+	0.317608i
$403$	−3.56248	+	3.56248i	−0.177460	+	0.177460i
$404$	12.9700			0.645283
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$	−29.6269	−	29.6269i	−1.46855	−	1.46855i
$408$	1.38896	−	1.38896i	0.0687635	−	0.0687635i
$409$	32.9343			1.62850			0.814248	−	0.580516i	$-0.197149\pi$
$409$	32.9343			1.62850			0.814248	+	0.580516i	$0.197149\pi$
$410$	4.09109	+	1.36370i	0.202045	+	0.0673482i
$411$			12.9787i			0.640192i
$412$	−8.82843	+	8.82843i	−0.434945	+	0.434945i
$413$		0			0
$414$			4.24264i			0.208514i
$415$	−2.51434	+	7.54303i	−0.123424	+	0.370273i
$416$		−	6.19212i		−	0.303594i
$417$	−13.2217	−	13.2217i	−0.647470	−	0.647470i
$418$	−11.5706	−	11.5706i	−0.565937	−	0.565937i
$419$	2.34315			0.114470			0.0572351	−	0.998361i	$-0.481772\pi$
$419$	2.34315			0.114470			0.0572351	+	0.998361i	$0.481772\pi$
$420$		0			0
$421$	−22.5654			−1.09977			−0.549885	−	0.835240i	$-0.685328\pi$
$421$	−22.5654			−1.09977			−0.549885	+	0.835240i	$0.685328\pi$
$422$	11.0772	+	11.0772i	0.539229	+	0.539229i
$423$	6.59588	+	6.59588i	0.320702	+	0.320702i
$424$			11.1918i			0.543519i
$425$	1.38896	+	9.72269i	0.0673742	+	0.471620i
$426$		−	14.9700i		−	0.725301i
$427$		0			0
$428$	−9.62113	+	9.62113i	−0.465055	+	0.465055i
$429$		−	29.6770i		−	1.43282i
$430$	8.25744	+	16.5149i	0.398209	+	0.796418i
$431$	−2.72792			−0.131399			−0.0656997	−	0.997839i	$-0.520928\pi$
$431$	−2.72792			−0.131399			−0.0656997	+	0.997839i	$0.520928\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−19.6211	−	19.6211i	−0.942931	−	0.942931i	0.0555258	−	0.998457i	$-0.482317\pi$
$433$	−19.6211	−	19.6211i	−0.942931	−	0.942931i	−0.998457	+	0.0555258i	$0.982317\pi$
$434$		0			0
$435$	−3.03139	−	1.01046i	−0.145344	−	0.0484480i
$436$	14.4348			0.691300
$437$	−10.2426	+	10.2426i	−0.489972	+	0.489972i
$438$	−4.81363	+	4.81363i	−0.230004	+	0.230004i
$439$	−26.8757			−1.28271			−0.641353	−	0.767246i	$-0.721626\pi$
$439$	−26.8757			−1.28271			−0.641353	+	0.767246i	$0.721626\pi$
$440$	−10.1669	−	3.38896i	−0.484686	−	0.161562i
$441$		0			0
$442$	8.60058	+	8.60058i	0.409088	+	0.409088i
$443$	−3.22209	+	3.22209i	−0.153086	+	0.153086i	−0.779495	−	0.626409i	$-0.784524\pi$
$443$	−3.22209	+	3.22209i	−0.153086	+	0.153086i	0.626409	+	0.779495i	$0.284524\pi$
$444$	8.74219			0.414886
$445$	9.97908	+	19.9582i	0.473054	+	0.946107i
$446$			12.3929i			0.586822i
$447$	1.31842	−	1.31842i	0.0623589	−	0.0623589i
$448$		0			0
$449$			5.12972i			0.242087i	0.992647	+	0.121043i	$0.0386240\pi$
$449$			5.12972i			0.242087i	−0.992647	+	0.121043i	$0.961376\pi$
$450$	0.707107	+	4.94975i	0.0333333	+	0.233333i
$451$		−	9.24301i		−	0.435237i
$452$	−0.0209247	−	0.0209247i	−0.000984217	−	0.000984217i
$453$	5.76311	+	5.76311i	0.270775	+	0.270775i
$454$	11.7283			0.550436
$455$		0			0
$456$	3.41421			0.159885
$457$	−0.908910	−	0.908910i	−0.0425170	−	0.0425170i	0.685529	−	0.728046i	$-0.259571\pi$
$457$	−0.908910	−	0.908910i	−0.0425170	−	0.0425170i	−0.728046	+	0.685529i	$0.759571\pi$
$458$	−13.5058	−	13.5058i	−0.631086	−	0.631086i
$459$			1.96428i			0.0916847i
$460$	−3.00000	+	9.00000i	−0.139876	+	0.419627i
$461$		−	18.0830i		−	0.842207i	−0.907013	−	0.421104i	$-0.861643\pi$
$461$		−	18.0830i		−	0.842207i	0.907013	−	0.421104i	$-0.138357\pi$
$462$		0			0
$463$	9.20116	−	9.20116i	0.427614	−	0.427614i	−0.460201	−	0.887815i	$-0.652223\pi$
$463$	9.20116	−	9.20116i	0.427614	−	0.427614i	0.887815	+	0.460201i	$0.152223\pi$
$464$			1.42901i			0.0663401i
$465$	−1.72597	−	0.575324i	−0.0800400	−	0.0266800i
$466$	−14.8999			−0.690223
$467$	0.878944	−	0.878944i	0.0406727	−	0.0406727i	−0.686478	−	0.727151i	$-0.740844\pi$
$467$	0.878944	−	0.878944i	0.0406727	−	0.0406727i	0.727151	+	0.686478i	$0.240844\pi$
$468$	4.37849	+	4.37849i	0.202396	+	0.202396i
$469$		0			0
$470$	9.32798	+	18.6560i	0.430267	+	0.860535i
$471$	−18.4853			−0.851757
$472$	−3.79271	+	3.79271i	−0.174573	+	0.174573i
$473$	27.9841	−	27.9841i	1.28671	−	1.28671i
$474$	−1.92856			−0.0885816
$475$	−10.2426	+	13.6569i	−0.469965	+	0.626619i
$476$		0			0
$477$	−7.91376	−	7.91376i	−0.362346	−	0.362346i
$478$	6.15065	−	6.15065i	0.281324	−	0.281324i
$479$	12.7065			0.580573			0.290287	−	0.956940i	$-0.406249\pi$
$479$	12.7065			0.580573			0.290287	+	0.956940i	$0.406249\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$			54.1327i			2.46824i
$482$	4.80280	−	4.80280i	0.218761	−	0.218761i
$483$		0			0
$484$			11.9700i			0.544092i
$485$	−33.6824	−	11.2275i	−1.52944	−	0.509813i
$486$			1.00000i			0.0453609i
$487$	0.0923663	+	0.0923663i	0.00418552	+	0.00418552i	0.709196	−	0.705011i	$-0.249058\pi$
$487$	0.0923663	+	0.0923663i	0.00418552	+	0.00418552i	−0.705011	+	0.709196i	$0.749058\pi$
$488$	−6.77791	−	6.77791i	−0.306822	−	0.306822i
$489$	4.93431			0.223137
$490$		0			0
$491$	33.8138			1.52599			0.762997	−	0.646402i	$-0.223727\pi$
$491$	33.8138			1.52599			0.762997	+	0.646402i	$0.223727\pi$
$492$	1.36370	+	1.36370i	0.0614802	+	0.0614802i
$493$	−1.98483	−	1.98483i	−0.0893923	−	0.0893923i
$494$			21.1412i			0.951189i
$495$	9.58541	−	4.79271i	0.430832	−	0.215416i
$496$			0.813631i			0.0365331i
$497$		0			0
$498$	−2.51434	+	2.51434i	−0.112670	+	0.112670i
$499$		−	5.20401i		−	0.232963i	−0.993193	−	0.116482i	$-0.962838\pi$
$499$		−	5.20401i		−	0.232963i	0.993193	−	0.116482i	$-0.0371616\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	17.0772			0.762953
$502$	6.60671	−	6.60671i	0.294872	−	0.294872i
$503$	21.4748	+	21.4748i	0.957515	+	0.957515i	0.999134	−	0.0416187i	$-0.0132515\pi$
$503$	21.4748	+	21.4748i	0.957515	+	0.957515i	−0.0416187	+	0.999134i	$0.513251\pi$
$504$		0			0
$505$	−25.9401	+	12.9700i	−1.15432	+	0.577159i
$506$	20.3337			0.903945
$507$	−17.9198	+	17.9198i	−0.795845	+	0.795845i
$508$	8.97003	−	8.97003i	0.397981	−	0.397981i
$509$	−11.0292			−0.488862			−0.244431	−	0.969667i	$-0.578601\pi$
$509$	−11.0292			−0.488862			−0.244431	+	0.969667i	$0.578601\pi$
$510$	−1.38896	+	4.16687i	−0.0615040	+	0.184512i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.41421	+	2.41421i	−0.106590	+	0.106590i
$514$	5.19788			0.229269
$515$	8.82843	−	26.4853i	0.389027	−	1.16708i
$516$			8.25744i			0.363513i
$517$	31.6121	−	31.6121i	1.39030	−	1.39030i
$518$		0			0
$519$		−	16.2123i		−	0.711641i
$520$	6.19212	+	12.3842i	0.271543	+	0.543085i
$521$		−	3.73696i		−	0.163719i	−0.996644	−	0.0818597i	$-0.973914\pi$
$521$		−	3.73696i		−	0.163719i	0.996644	−	0.0818597i	$-0.0260859\pi$
$522$	−1.01046	−	1.01046i	−0.0442267	−	0.0442267i
$523$	26.4849	+	26.4849i	1.15810	+	1.15810i	0.984883	+	0.173221i	$0.0554176\pi$
$523$	26.4849	+	26.4849i	1.15810	+	1.15810i	0.173221	+	0.984883i	$0.444582\pi$
$524$	−0.293157			−0.0128066
$525$		0			0
$526$	12.4429			0.542536
$527$	−1.13010	−	1.13010i	−0.0492278	−	0.0492278i
$528$	−3.38896	−	3.38896i	−0.147485	−	0.147485i
$529$			5.00000i			0.217391i
$530$	−11.1918	−	22.3835i	−0.486139	−	0.972277i
$531$		−	5.36370i		−	0.232765i
$532$		0			0
$533$	−8.44418	+	8.44418i	−0.365758	+	0.365758i
$534$			9.97908i			0.431837i
$535$	9.62113	−	28.8634i	0.415958	−	1.24787i
$536$	−9.00575			−0.388989
$537$	−11.3027	+	11.3027i	−0.487748	+	0.487748i
$538$	−14.0702	−	14.0702i	−0.606608	−	0.606608i
$539$		0			0
$540$	−0.707107	+	2.12132i	−0.0304290	+	0.0912871i
$541$	29.0279			1.24801			0.624004	−	0.781421i	$-0.285505\pi$
$541$	29.0279			1.24801			0.624004	+	0.781421i	$0.285505\pi$
$542$	13.8742	−	13.8742i	0.595949	−	0.595949i
$543$	−7.29226	+	7.29226i	−0.312941	+	0.312941i
$544$	1.96428			0.0842178
$545$	−28.8695	+	14.4348i	−1.23663	+	0.618317i
$546$		0			0
$547$	26.6579	+	26.6579i	1.13981	+	1.13981i	0.988484	+	0.151326i	$0.0483542\pi$
$547$	26.6579	+	26.6579i	1.13981	+	1.13981i	0.151326	+	0.988484i	$0.451646\pi$
$548$	−9.17733	+	9.17733i	−0.392036	+	0.392036i
$549$	9.58541			0.409095
$550$	23.7227	−	3.38896i	1.01154	−	0.144506i
$551$		−	4.87894i		−	0.207850i
$552$	−3.00000	+	3.00000i	−0.127688	+	0.127688i
$553$		0			0
$554$		−	16.0054i		−	0.680003i
$555$	−17.4844	+	8.74219i	−0.742171	+	0.371085i
$556$		−	18.6983i		−	0.792986i
$557$	14.7488	+	14.7488i	0.624929	+	0.624929i	0.946788	−	0.321859i	$-0.104308\pi$
$557$	14.7488	+	14.7488i	0.624929	+	0.624929i	−0.321859	+	0.946788i	$0.604308\pi$
$558$	−0.575324	−	0.575324i	−0.0243554	−	0.0243554i
$559$	−51.1311			−2.16261
$560$		0			0
$561$	9.41421			0.397468
$562$	−10.9491	−	10.9491i	−0.461860	−	0.461860i
$563$	−12.8986	−	12.8986i	−0.543611	−	0.543611i	0.380975	−	0.924585i	$-0.375589\pi$
$563$	−12.8986	−	12.8986i	−0.543611	−	0.543611i	−0.924585	+	0.380975i	$0.875589\pi$
$564$			9.32798i			0.392779i
$565$	0.0627742	+	0.0209247i	0.00264093	+	0.000880310i
$566$			12.2845i			0.516356i
$567$		0			0
$568$	10.5854	−	10.5854i	0.444154	−	0.444154i
$569$		−	36.7562i		−	1.54090i	−0.637499	−	0.770451i	$-0.720031\pi$
$569$		−	36.7562i		−	1.54090i	0.637499	−	0.770451i	$-0.279969\pi$
$570$	−6.82843	+	3.41421i	−0.286011	+	0.143006i
$571$	−24.8266			−1.03896			−0.519481	−	0.854482i	$-0.673875\pi$
$571$	−24.8266			−1.03896			−0.519481	+	0.854482i	$0.673875\pi$
$572$	20.9848	−	20.9848i	0.877420	−	0.877420i
$573$	10.2632	+	10.2632i	0.428751	+	0.428751i
$574$		0			0
$575$	−3.00000	−	21.0000i	−0.125109	−	0.875761i
$576$	1.00000			0.0416667
$577$	−13.4762	+	13.4762i	−0.561023	+	0.561023i	−0.929598	−	0.368575i	$-0.879846\pi$
$577$	−13.4762	+	13.4762i	−0.561023	+	0.561023i	0.368575	+	0.929598i	$0.379846\pi$
$578$	9.29252	−	9.29252i	0.386518	−	0.386518i
$579$	−7.34277			−0.305155
$580$	−1.42901	−	2.85802i	−0.0593364	−	0.118673i
$581$		0			0
$582$	−11.2275	−	11.2275i	−0.465394	−	0.465394i
$583$	−37.9283	+	37.9283i	−1.57083	+	1.57083i
$584$	−6.80750			−0.281696
$585$	−13.1355	−	4.37849i	−0.543085	−	0.181028i
$586$		−	30.8272i		−	1.27346i
$587$	−1.72777	+	1.72777i	−0.0713126	+	0.0713126i	−0.741864	−	0.670551i	$-0.766058\pi$
$587$	−1.72777	+	1.72777i	−0.0713126	+	0.0713126i	0.670551	+	0.741864i	$0.266058\pi$
$588$		0			0
$589$		−	2.77791i		−	0.114462i
$590$	3.79271	−	11.3781i	0.156143	−	0.468430i
$591$		−	16.6560i		−	0.685134i
$592$	6.18166	+	6.18166i	0.254065	+	0.254065i
$593$	−6.64602	−	6.64602i	−0.272919	−	0.272919i	0.557355	−	0.830274i	$-0.311816\pi$
$593$	−6.64602	−	6.64602i	−0.272919	−	0.272919i	−0.830274	+	0.557355i	$0.811816\pi$
$594$	4.79271			0.196647
$595$		0			0
$596$	1.86452			0.0763738
$597$	1.50478	+	1.50478i	0.0615867	+	0.0615867i
$598$	−18.5764	−	18.5764i	−0.759644	−	0.759644i
$599$		−	43.1818i		−	1.76436i	−0.470912	−	0.882180i	$-0.656075\pi$
$599$		−	43.1818i		−	1.76436i	0.470912	−	0.882180i	$-0.343925\pi$
$600$	−3.00000	+	4.00000i	−0.122474	+	0.163299i
$601$			40.8953i			1.66815i	0.551648	+	0.834077i	$0.313999\pi$
$601$			40.8953i			1.66815i	−0.551648	+	0.834077i	$0.686001\pi$
$602$		0			0
$603$	6.36803	−	6.36803i	0.259326	−	0.259326i
$604$			8.15027i			0.331630i
$605$	−11.9700	−	23.9401i	−0.486651	−	0.973302i
$606$	−12.9700			−0.526872
$607$	−16.2569	+	16.2569i	−0.659848	+	0.659848i	−0.955344	−	0.295496i	$-0.904515\pi$
$607$	−16.2569	+	16.2569i	−0.659848	+	0.659848i	0.295496	+	0.955344i	$0.404515\pi$
$608$	2.41421	+	2.41421i	0.0979093	+	0.0979093i
$609$		0			0
$610$	20.3337	+	6.77791i	0.823289	+	0.274430i
$611$	−57.7600			−2.33672
$612$	−1.38896	+	1.38896i	−0.0561452	+	0.0561452i
$613$	−18.8228	+	18.8228i	−0.760246	+	0.760246i	−0.976367	−	0.216120i	$-0.930660\pi$
$613$	−18.8228	+	18.8228i	−0.760246	+	0.760246i	0.216120	+	0.976367i	$0.430660\pi$
$614$	4.38425			0.176934
$615$	−4.09109	−	1.36370i	−0.164969	−	0.0549896i
$616$		0			0
$617$	23.9343	+	23.9343i	0.963559	+	0.963559i	0.999359	−	0.0357998i	$-0.0113979\pi$
$617$	23.9343	+	23.9343i	0.963559	+	0.963559i	−0.0357998	+	0.999359i	$0.511398\pi$
$618$	8.82843	−	8.82843i	0.355131	−	0.355131i
$619$	−41.9980			−1.68804			−0.844021	−	0.536311i	$-0.819818\pi$
$619$	−41.9980			−1.68804			−0.844021	+	0.536311i	$0.819818\pi$
$620$	−0.813631	−	1.62726i	−0.0326762	−	0.0653524i
$621$		−	4.24264i		−	0.170251i
$622$	18.8925	−	18.8925i	0.757519	−	0.757519i
$623$		0			0
$624$			6.19212i			0.247883i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		−	4.79884i		−	0.191800i
$627$	11.5706	+	11.5706i	0.462086	+	0.462086i
$628$	−13.0711	−	13.0711i	−0.521592	−	0.521592i
$629$	−17.1721			−0.684697
$630$		0			0
$631$	−39.8053			−1.58462			−0.792312	−	0.610116i	$-0.791123\pi$
$631$	−39.8053			−1.58462			−0.792312	+	0.610116i	$0.791123\pi$
$632$	−1.36370	−	1.36370i	−0.0542449	−	0.0542449i
$633$	−11.0772	−	11.0772i	−0.440279	−	0.440279i
$634$			27.4129i			1.08871i
$635$	−8.97003	+	26.9101i	−0.355965	+	1.06789i
$636$		−	11.1918i		−	0.443782i
$637$		0			0
$638$	−4.84285	+	4.84285i	−0.191730	+	0.191730i
$639$			14.9700i			0.592205i
$640$	2.12132	+	0.707107i	0.0838525	+	0.0279508i
$641$	5.25452			0.207541			0.103771	−	0.994601i	$-0.466909\pi$
$641$	5.25452			0.207541			0.103771	+	0.994601i	$0.466909\pi$
$642$	9.62113	−	9.62113i	0.379716	−	0.379716i
$643$	−10.6974	−	10.6974i	−0.421865	−	0.421865i	0.463980	−	0.885846i	$-0.346421\pi$
$643$	−10.6974	−	10.6974i	−0.421865	−	0.421865i	−0.885846	+	0.463980i	$0.846421\pi$
$644$		0			0
$645$	−8.25744	−	16.5149i	−0.325136	−	0.650273i
$646$	−6.70647			−0.263862
$647$	−11.8180	+	11.8180i	−0.464612	+	0.464612i	−0.900164	−	0.435552i	$-0.856553\pi$
$647$	−11.8180	+	11.8180i	−0.464612	+	0.464612i	0.435552	+	0.900164i	$0.356553\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−25.7066			−1.00907
$650$	−24.7685	−	18.5764i	−0.971500	−	0.728625i
$651$		0			0
$652$	3.48909	+	3.48909i	0.136643	+	0.136643i
$653$	17.2275	−	17.2275i	0.674163	−	0.674163i	−0.284510	−	0.958673i	$-0.591831\pi$
$653$	17.2275	−	17.2275i	0.674163	−	0.674163i	0.958673	+	0.284510i	$0.0918309\pi$
$654$	−14.4348			−0.564444
$655$	0.586315	−	0.293157i	0.0229092	−	0.0114546i
$656$			1.92856i			0.0752976i
$657$	4.81363	−	4.81363i	0.187798	−	0.187798i
$658$		0			0
$659$		−	22.3904i		−	0.872205i	−0.899897	−	0.436103i	$-0.856358\pi$
$659$		−	22.3904i		−	0.872205i	0.899897	−	0.436103i	$-0.143642\pi$
$660$	10.1669	+	3.38896i	0.395745	+	0.131915i
$661$		−	1.18383i		−	0.0460457i	−0.999735	−	0.0230228i	$-0.992671\pi$
$661$		−	1.18383i		−	0.0460457i	0.999735	−	0.0230228i	$-0.00732904\pi$
$662$	−23.8133	−	23.8133i	−0.925529	−	0.925529i
$663$	−8.60058	−	8.60058i	−0.334019	−	0.334019i
$664$	−3.55582			−0.137993
$665$		0			0
$666$	−8.74219			−0.338753
$667$	4.28703	+	4.28703i	0.165994	+	0.165994i
$668$	12.0754	+	12.0754i	0.467211	+	0.467211i
$669$		−	12.3929i		−	0.479138i
$670$	18.0115	−	9.00575i	0.695845	−	0.347923i
$671$		−	45.9401i		−	1.77350i
$672$		0			0
$673$	24.4257	−	24.4257i	0.941542	−	0.941542i	−0.0568408	−	0.998383i	$-0.518103\pi$
$673$	24.4257	−	24.4257i	0.941542	−	0.941542i	0.998383	+	0.0568408i	$0.0181027\pi$
$674$		−	8.65723i		−	0.333464i
$675$	−0.707107	−	4.94975i	−0.0272166	−	0.190516i
$676$	−25.3424			−0.974708
$677$	8.12158	−	8.12158i	0.312138	−	0.312138i	−0.533599	−	0.845737i	$-0.679161\pi$
$677$	8.12158	−	8.12158i	0.312138	−	0.312138i	0.845737	+	0.533599i	$0.179161\pi$
$678$	0.0209247	+	0.0209247i	0.000803610	+	0.000803610i
$679$		0			0
$680$	−3.92856	+	1.96428i	−0.150653	+	0.0753267i
$681$	−11.7283			−0.449429
$682$	−2.75736	+	2.75736i	−0.105585	+	0.105585i
$683$	−3.42235	+	3.42235i	−0.130953	+	0.130953i	−0.769545	−	0.638592i	$-0.779517\pi$
$683$	−3.42235	+	3.42235i	−0.130953	+	0.130953i	0.638592	+	0.769545i	$0.279517\pi$
$684$	−3.41421			−0.130546
$685$	9.17733	−	27.5320i	0.350648	−	1.05194i
$686$		0			0
$687$	13.5058	+	13.5058i	0.515280	+	0.515280i
$688$	−5.83889	+	5.83889i	−0.222606	+	0.222606i
$689$	69.3007			2.64015
$690$	3.00000	−	9.00000i	0.114208	−	0.342624i
$691$		−	7.64587i		−	0.290863i	−0.989368	−	0.145431i	$-0.953543\pi$
$691$		−	7.64587i		−	0.290863i	0.989368	−	0.145431i	$-0.0464570\pi$
$692$	11.4638	−	11.4638i	0.435789	−	0.435789i
$693$		0			0
$694$		−	15.7857i		−	0.599216i
$695$	18.6983	+	37.3967i	0.709268	+	1.41854i
$696$		−	1.42901i		−	0.0541665i
$697$	−2.67868	−	2.67868i	−0.101462	−	0.101462i
$698$	3.24301	+	3.24301i	0.122750	+	0.122750i
$699$	14.8999			0.563565
$700$		0			0
$701$	−6.43752			−0.243142			−0.121571	−	0.992583i	$-0.538793\pi$
$701$	−6.43752			−0.243142			−0.121571	+	0.992583i	$0.538793\pi$
$702$	−4.37849	−	4.37849i	−0.165256	−	0.165256i
$703$	−21.1055	−	21.1055i	−0.796009	−	0.796009i
$704$		−	4.79271i		−	0.180632i
$705$	−9.32798	−	18.6560i	−0.351312	−	0.702624i
$706$		−	14.9930i		−	0.564268i
$707$		0			0
$708$	3.79271	−	3.79271i	0.142539	−	0.142539i
$709$			27.9610i			1.05010i	0.851072	+	0.525049i	$0.175953\pi$
$709$			27.9610i			1.05010i	−0.851072	+	0.525049i	$0.824047\pi$
$710$	−10.5854	+	31.7562i	−0.397263	+	1.19179i
$711$	1.92856			0.0723266
$712$	−7.05627	+	7.05627i	−0.264445	+	0.264445i
$713$	2.44089	+	2.44089i	0.0914122	+	0.0914122i
$714$		0			0
$715$	−20.9848	+	62.9545i	−0.784788	+	2.35436i
$716$	−15.9845			−0.597367
$717$	−6.15065	+	6.15065i	−0.229700	+	0.229700i
$718$	17.9996	−	17.9996i	0.671740	−	0.671740i
$719$	7.87879			0.293829			0.146915	−	0.989149i	$-0.453066\pi$
$719$	7.87879			0.293829			0.146915	+	0.989149i	$0.453066\pi$
$720$	−2.00000	+	1.00000i	−0.0745356	+	0.0372678i
$721$		0			0
$722$	5.19239	+	5.19239i	0.193241	+	0.193241i
$723$	−4.80280	+	4.80280i	−0.178618	+	0.178618i
$724$	−10.3128			−0.383272
$725$	5.71604	+	4.28703i	0.212288	+	0.159216i
$726$		−	11.9700i		−	0.444250i
$727$	−18.9147	+	18.9147i	−0.701506	+	0.701506i	−0.964734	−	0.263228i	$-0.915213\pi$
$727$	−18.9147	+	18.9147i	−0.701506	+	0.701506i	0.263228	+	0.964734i	$0.415213\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	13.6150	−	6.80750i	0.503914	−	0.251957i
$731$		−	16.2199i		−	0.599915i
$732$	6.77791	+	6.77791i	0.250519	+	0.250519i
$733$	−8.42325	−	8.42325i	−0.311120	−	0.311120i	0.534223	−	0.845343i	$-0.320604\pi$
$733$	−8.42325	−	8.42325i	−0.311120	−	0.311120i	−0.845343	+	0.534223i	$0.820604\pi$
$734$	−4.63577			−0.171110
$735$		0			0
$736$	−4.24264			−0.156386
$737$	−30.5201	−	30.5201i	−1.12422	−	1.12422i
$738$	−1.36370	−	1.36370i	−0.0501984	−	0.0501984i
$739$		−	41.5341i		−	1.52786i	−0.645300	−	0.763929i	$-0.723268\pi$
$739$		−	41.5341i		−	1.52786i	0.645300	−	0.763929i	$-0.276732\pi$
$740$	−18.5450	−	6.18166i	−0.681727	−	0.227242i
$741$		−	21.1412i		−	0.776643i
$742$		0			0
$743$	13.1412	−	13.1412i	0.482105	−	0.482105i	−0.423698	−	0.905803i	$-0.639268\pi$
$743$	13.1412	−	13.1412i	0.482105	−	0.482105i	0.905803	+	0.423698i	$0.139268\pi$
$744$		−	0.813631i		−	0.0298292i
$745$	−3.72904	+	1.86452i	−0.136622	+	0.0683108i
$746$	−23.9845			−0.878133
$747$	2.51434	−	2.51434i	0.0919951	−	0.0919951i
$748$	6.65685	+	6.65685i	0.243399	+	0.243399i
$749$		0			0
$750$	2.00000	−	11.0000i	0.0730297	−	0.401663i
$751$	−43.3038			−1.58018			−0.790088	−	0.612993i	$-0.789965\pi$
$751$	−43.3038			−1.58018			−0.790088	+	0.612993i	$0.789965\pi$
$752$	−6.59588	+	6.59588i	−0.240527	+	0.240527i
$753$	−6.60671	+	6.60671i	−0.240762	+	0.240762i
$754$	8.84860			0.322247
$755$	−8.15027	−	16.3005i	−0.296619	−	0.593238i
$756$		0			0
$757$	−22.4945	−	22.4945i	−0.817575	−	0.817575i	0.168181	−	0.985756i	$-0.446211\pi$
$757$	−22.4945	−	22.4945i	−0.817575	−	0.817575i	−0.985756	+	0.168181i	$0.946211\pi$
$758$	−11.1573	+	11.1573i	−0.405252	+	0.405252i
$759$	−20.3337			−0.738068
$760$	−7.24264	−	2.41421i	−0.262718	−	0.0875727i
$761$			37.7275i			1.36762i	0.729659	+	0.683811i	$0.239679\pi$
$761$			37.7275i			1.36762i	−0.729659	+	0.683811i	$0.760321\pi$
$762$	−8.97003	+	8.97003i	−0.324950	+	0.324950i
$763$		0			0
$764$			14.5143i			0.525111i
$765$	1.38896	−	4.16687i	0.0502178	−	0.150653i
$766$		−	10.8636i		−	0.392519i
$767$	23.4849	+	23.4849i	0.847991	+	0.847991i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	24.0564			0.867497			0.433748	−	0.901034i	$-0.357191\pi$
$769$	24.0564			0.867497			0.433748	+	0.901034i	$0.357191\pi$
$770$		0			0
$771$	−5.19788			−0.187197
$772$	−5.19212	−	5.19212i	−0.186869	−	0.186869i
$773$	−13.5554	−	13.5554i	−0.487556	−	0.487556i	0.419979	−	0.907534i	$-0.362038\pi$
$773$	−13.5554	−	13.5554i	−0.487556	−	0.487556i	−0.907534	+	0.419979i	$0.862038\pi$
$774$		−	8.25744i		−	0.296807i
$775$	3.25452	+	2.44089i	0.116906	+	0.0876795i
$776$		−	15.8780i		−	0.569988i
$777$		0			0
$778$	7.82462	−	7.82462i	0.280526	−	0.280526i
$779$		−	6.58451i		−	0.235915i
$780$	−6.19212	−	12.3842i	−0.221714	−	0.443427i
$781$	71.7470			2.56731
$782$	5.89284	−	5.89284i	0.210727	−	0.210727i
$783$	1.01046	+	1.01046i	0.0361110	+	0.0361110i
$784$		0			0
$785$	39.2132	+	13.0711i	1.39958	+	0.466526i
$786$	0.293157			0.0104566
$787$	7.95815	−	7.95815i	0.283677	−	0.283677i	−0.550896	−	0.834574i	$-0.685714\pi$
$787$	7.95815	−	7.95815i	0.283677	−	0.283677i	0.834574	+	0.550896i	$0.185714\pi$
$788$	11.7775	−	11.7775i	0.419557	−	0.419557i
$789$	−12.4429			−0.442979
$790$	4.09109	+	1.36370i	0.145554	+	0.0485182i
$791$		0			0
$792$	3.38896	+	3.38896i	0.120421	+	0.120421i
$793$	−41.9697	+	41.9697i	−1.49039	+	1.49039i
$794$	3.17157			0.112555
$795$	11.1918	+	22.3835i	0.396930	+	0.793861i
$796$			2.12809i			0.0754280i
$797$	−28.3339	+	28.3339i	−1.00364	+	1.00364i	−0.00364437	+	0.999993i	$0.501160\pi$
$797$	−28.3339	+	28.3339i	−1.00364	+	1.00364i	−0.999993	+	0.00364437i	$0.998840\pi$
$798$		0			0
$799$		−	18.3227i		−	0.648212i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		−	9.97908i		−	0.352593i
$802$	−21.4339	−	21.4339i	−0.756856	−	0.756856i
$803$	−23.0703	−	23.0703i	−0.814134	−	0.814134i
$804$	9.00575			0.317608
$805$		0			0
$806$	5.03810			0.177460
$807$	14.0702	+	14.0702i	0.495293	+	0.495293i
$808$	−9.17120	−	9.17120i	−0.322642	−	0.322642i
$809$		−	54.0815i		−	1.90140i	−0.310108	−	0.950701i	$-0.600365\pi$
$809$		−	54.0815i		−	1.90140i	0.310108	−	0.950701i	$-0.399635\pi$
$810$	0.707107	−	2.12132i	0.0248452	−	0.0745356i
$811$		−	18.7583i		−	0.658692i	−0.944209	−	0.329346i	$-0.893172\pi$
$811$		−	18.7583i		−	0.658692i	0.944209	−	0.329346i	$-0.106828\pi$
$812$		0			0
$813$	−13.8742	+	13.8742i	−0.486591	+	0.486591i
$814$			41.8987i			1.46855i
$815$	−10.4673	−	3.48909i	−0.366652	−	0.122217i
$816$	−1.96428			−0.0687635
$817$	19.9352	−	19.9352i	0.697445	−	0.697445i
$818$	−23.2881	−	23.2881i	−0.814248	−	0.814248i
$819$		0			0
$820$	−1.92856	−	3.85712i	−0.0673482	−	0.134696i
$821$	5.32798			0.185948			0.0929738	−	0.995669i	$-0.470363\pi$
$821$	5.32798			0.185948			0.0929738	+	0.995669i	$0.470363\pi$
$822$	9.17733	−	9.17733i	0.320096	−	0.320096i
$823$	25.0206	−	25.0206i	0.872162	−	0.872162i	−0.120546	−	0.992708i	$-0.538465\pi$
$823$	25.0206	−	25.0206i	0.872162	−	0.872162i	0.992708	+	0.120546i	$0.0384646\pi$
$824$	12.4853			0.434945
$825$	−23.7227	+	3.38896i	−0.825918	+	0.117988i
$826$		0			0
$827$	1.54969	+	1.54969i	0.0538881	+	0.0538881i	0.733537	−	0.679649i	$-0.237868\pi$
$827$	1.54969	+	1.54969i	0.0538881	+	0.0538881i	−0.679649	+	0.733537i	$0.737868\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	−42.9402			−1.49138			−0.745688	−	0.666296i	$-0.767879\pi$
$829$	−42.9402			−1.49138			−0.745688	+	0.666296i	$0.767879\pi$
$830$	7.11164	−	3.55582i	0.246849	−	0.123424i
$831$			16.0054i			0.555221i
$832$	−4.37849	+	4.37849i	−0.151797	+	0.151797i
$833$		0			0
$834$			18.6983i			0.647470i
$835$	−36.2262	−	12.0754i	−1.25366	−	0.417886i
$836$			16.3633i			0.565937i
$837$	0.575324	+	0.575324i	0.0198861	+	0.0198861i
$838$	−1.65685	−	1.65685i	−0.0572351	−	0.0572351i
$839$	−21.9697			−0.758477			−0.379238	−	0.925299i	$-0.623814\pi$
$839$	−21.9697			−0.758477			−0.379238	+	0.925299i	$0.623814\pi$
$840$		0			0
$841$	26.9579			0.929584
$842$	15.9561	+	15.9561i	0.549885	+	0.549885i
$843$	10.9491	+	10.9491i	0.377107	+	0.377107i
$844$		−	15.6655i		−	0.539229i
$845$	50.6848	−	25.3424i	1.74361	−	0.871805i
$846$		−	9.32798i		−	0.320702i
$847$		0			0
$848$	7.91376	−	7.91376i	0.271760	−	0.271760i
$849$		−	12.2845i		−	0.421603i
$850$	5.89284	−	7.85712i	0.202123	−	0.269497i
$851$	37.0900			1.27143
$852$	−10.5854	+	10.5854i	−0.362650	+	0.362650i
$853$	30.4644	+	30.4644i	1.04308	+	1.04308i	0.999029	+	0.0440504i	$0.0140262\pi$
$853$	30.4644	+	30.4644i	1.04308	+	1.04308i	0.0440504	+	0.999029i	$0.485974\pi$
$854$		0			0
$855$	6.82843	−	3.41421i	0.233527	−	0.116764i
$856$	13.6063			0.465055
$857$	−13.2522	+	13.2522i	−0.452687	+	0.452687i	−0.896245	−	0.443559i	$-0.853716\pi$
$857$	−13.2522	+	13.2522i	−0.452687	+	0.452687i	0.443559	+	0.896245i	$0.353716\pi$
$858$	−20.9848	+	20.9848i	−0.716410	+	0.716410i
$859$	41.9283			1.43058			0.715288	−	0.698830i	$-0.246295\pi$
$859$	41.9283			1.43058			0.715288	+	0.698830i	$0.246295\pi$
$860$	5.83889	−	17.5167i	0.199104	−	0.597313i
$861$		0			0
$862$	1.92893	+	1.92893i	0.0656997	+	0.0656997i
$863$	38.2419	−	38.2419i	1.30177	−	1.30177i	0.374571	−	0.927198i	$-0.377790\pi$
$863$	38.2419	−	38.2419i	1.30177	−	1.30177i	0.927198	−	0.374571i	$-0.122210\pi$
$864$	−1.00000			−0.0340207
$865$	−11.4638	+	34.3915i	−0.389782	+	1.16935i
$866$			27.7485i			0.942931i
$867$	−9.29252	+	9.29252i	−0.315591	+	0.315591i
$868$		0			0
$869$		−	9.24301i		−	0.313548i
$870$	1.42901	+	2.85802i	0.0484480	+	0.0968959i
$871$			55.7648i			1.88952i
$872$	−10.2069	−	10.2069i	−0.345650	−	0.345650i
$873$	11.2275	+	11.2275i	0.379992	+	0.379992i
$874$	14.4853			0.489972
$875$		0			0
$876$	6.80750			0.230004
$877$	16.7669	+	16.7669i	0.566179	+	0.566179i	0.931056	−	0.364877i	$-0.118889\pi$
$877$	16.7669	+	16.7669i	0.566179	+	0.566179i	−0.364877	+	0.931056i	$0.618889\pi$
$878$	19.0040	+	19.0040i	0.641353	+	0.641353i
$879$			30.8272i			1.03977i
$880$	4.79271	+	9.58541i	0.161562	+	0.323124i
$881$		−	18.7057i		−	0.630212i	−0.949057	−	0.315106i	$-0.897960\pi$
$881$		−	18.7057i		−	0.630212i	0.949057	−	0.315106i	$-0.102040\pi$
$882$		0			0
$883$	26.4892	−	26.4892i	0.891434	−	0.891434i	−0.103224	−	0.994658i	$-0.532916\pi$
$883$	26.4892	−	26.4892i	0.891434	−	0.891434i	0.994658	+	0.103224i	$0.0329159\pi$
$884$		−	12.1631i		−	0.409088i
$885$	−3.79271	+	11.3781i	−0.127490	+	0.382471i
$886$	4.55672			0.153086
$887$	−16.2175	+	16.2175i	−0.544532	+	0.544532i	−0.924854	−	0.380322i	$-0.875813\pi$
$887$	−16.2175	+	16.2175i	−0.544532	+	0.544532i	0.380322	+	0.924854i	$0.375813\pi$
$888$	−6.18166	−	6.18166i	−0.207443	−	0.207443i
$889$		0			0
$890$	7.05627	−	21.1688i	0.236527	−	0.709580i
$891$	−4.79271			−0.160562
$892$	8.76311	−	8.76311i	0.293411	−	0.293411i
$893$	22.5197	−	22.5197i	0.753594	−	0.753594i
$894$	−1.86452			−0.0623589
$895$	31.9689	−	15.9845i	1.06860	−	0.534301i
$896$		0			0
$897$	18.5764	+	18.5764i	0.620247	+	0.620247i
$898$	3.62726	−	3.62726i	0.121043	−	0.121043i
$899$	−1.16269			−0.0387778
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$			21.9837i			0.732384i
$902$	−6.53580	+	6.53580i	−0.217618	+	0.217618i
$903$		0			0
$904$			0.0295921i			0.000984217i
$905$	20.6256	−	10.3128i	0.685619	−	0.342809i
$906$		−	8.15027i		−	0.270775i
$907$	22.2872	+	22.2872i	0.740033	+	0.740033i	0.972584	−	0.232551i	$-0.0747072\pi$
$907$	22.2872	+	22.2872i	0.740033	+	0.740033i	−0.232551	+	0.972584i	$0.574707\pi$
$908$	−8.29316	−	8.29316i	−0.275218	−	0.275218i
$909$	12.9700			0.430189
$910$		0			0
$911$	−39.2821			−1.30147			−0.650737	−	0.759303i	$-0.725540\pi$
$911$	−39.2821			−1.30147			−0.650737	+	0.759303i	$0.725540\pi$
$912$	−2.41421	−	2.41421i	−0.0799426	−	0.0799426i
$913$	−12.0505	−	12.0505i	−0.398814	−	0.398814i
$914$			1.28539i			0.0425170i
$915$	−20.3337	−	6.77791i	−0.672212	−	0.224071i
$916$			19.1001i			0.631086i
$917$		0			0
$918$	1.38896	−	1.38896i	0.0458424	−	0.0458424i
$919$		−	6.33320i		−	0.208913i	−0.994529	−	0.104457i	$-0.966690\pi$
$919$		−	6.33320i		−	0.208913i	0.994529	−	0.104457i	$-0.0333103\pi$
$920$	8.48528	−	4.24264i	0.279751	−	0.139876i
$921$	−4.38425			−0.144466
$922$	−12.7866	+	12.7866i	−0.421104	+	0.421104i
$923$	−65.5462	−	65.5462i	−2.15748	−	2.15748i
$924$		0			0
$925$	43.2716	−	6.18166i	1.42276	−	0.203252i
$926$	−13.0124			−0.427614
$927$	−8.82843	+	8.82843i	−0.289964	+	0.289964i
$928$	1.01046	−	1.01046i	0.0331701	−	0.0331701i
$929$	13.8694			0.455039			0.227520	−	0.973773i	$-0.426938\pi$
$929$	13.8694			0.455039			0.227520	+	0.973773i	$0.426938\pi$
$930$	0.813631	+	1.62726i	0.0266800	+	0.0533600i
$931$		0			0
$932$	10.5358	+	10.5358i	0.345112	+	0.345112i
$933$	−18.8925	+	18.8925i	−0.618512	+	0.618512i
$934$	−1.24301			−0.0406727
$935$	−19.9706	−	6.65685i	−0.653107	−	0.217702i
$936$		−	6.19212i		−	0.202396i
$937$	41.3839	−	41.3839i	1.35195	−	1.35195i	0.468476	−	0.883476i	$-0.344803\pi$
$937$	41.3839	−	41.3839i	1.35195	−	1.35195i	0.883476	−	0.468476i	$-0.155197\pi$
$938$		0			0
$939$			4.79884i			0.156604i
$940$	6.59588	−	19.7876i	0.215134	−	0.645401i
$941$		−	29.0693i		−	0.947631i	−0.880624	−	0.473815i	$-0.842876\pi$
$941$		−	29.0693i		−	0.947631i	0.880624	−	0.473815i	$-0.157124\pi$
$942$	13.0711	+	13.0711i	0.425878	+	0.425878i
$943$	5.78568	+	5.78568i	0.188408	+	0.188408i
$944$	5.36370			0.174573
$945$		0			0
$946$	−39.5755			−1.28671
$947$	−5.27261	−	5.27261i	−0.171337	−	0.171337i	0.616230	−	0.787566i	$-0.288659\pi$
$947$	−5.27261	−	5.27261i	−0.171337	−	0.171337i	−0.787566	+	0.616230i	$0.788659\pi$
$948$	1.36370	+	1.36370i	0.0442908	+	0.0442908i
$949$			42.1529i			1.36834i
$950$	16.8995	−	2.41421i	0.548292	−	0.0783274i
$951$		−	27.4129i		−	0.888925i
$952$		0			0
$953$	−23.5493	+	23.5493i	−0.762837	+	0.762837i	−0.976834	−	0.213997i	$-0.931352\pi$
$953$	−23.5493	+	23.5493i	−0.762837	+	0.762837i	0.213997	+	0.976834i	$0.431352\pi$
$954$			11.1918i			0.362346i
$955$	−14.5143	−	29.0287i	−0.469673	−	0.939346i
$956$	−8.69833			−0.281324
$957$	4.84285	−	4.84285i	0.156547	−	0.156547i
$958$	−8.98483	−	8.98483i	−0.290287	−	0.290287i
$959$		0			0
$960$	−2.12132	−	0.707107i	−0.0684653	−	0.0228218i
$961$	30.3380			0.978645
$962$	38.2776	−	38.2776i	1.23412	−	1.23412i
$963$	−9.62113	+	9.62113i	−0.310037	+	0.310037i
$964$	−6.79218			−0.218761
$965$	15.5764	+	5.19212i	0.501421	+	0.167140i
$966$		0			0
$967$	−21.2719	−	21.2719i	−0.684057	−	0.684057i	0.276855	−	0.960912i	$-0.410708\pi$
$967$	−21.2719	−	21.2719i	−0.684057	−	0.684057i	−0.960912	+	0.276855i	$0.910708\pi$
$968$	8.46409	−	8.46409i	0.272046	−	0.272046i
$969$	6.70647			0.215443
$970$	15.8780	+	31.7561i	0.509813	+	1.01963i
$971$		−	8.07069i		−	0.259001i	−0.991579	−	0.129500i	$-0.958663\pi$
$971$		−	8.07069i		−	0.259001i	0.991579	−	0.129500i	$-0.0413374\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$		0			0
$974$		−	0.130626i		−	0.00418552i
$975$	24.7685	+	18.5764i	0.793227	+	0.594920i
$976$			9.58541i			0.306822i
$977$	−18.1531	−	18.1531i	−0.580770	−	0.580770i	0.354345	−	0.935115i	$-0.384704\pi$
$977$	−18.1531	−	18.1531i	−0.580770	−	0.580770i	−0.935115	+	0.354345i	$0.884704\pi$
$978$	−3.48909	−	3.48909i	−0.111569	−	0.111569i
$979$	−47.8268			−1.52855
$980$		0			0
$981$	14.4348			0.460867
$982$	−23.9100	−	23.9100i	−0.762997	−	0.762997i
$983$	14.6311	+	14.6311i	0.466659	+	0.466659i	0.900830	−	0.434172i	$-0.142959\pi$
$983$	14.6311	+	14.6311i	0.466659	+	0.466659i	−0.434172	+	0.900830i	$0.642959\pi$
$984$		−	1.92856i		−	0.0614802i
$985$	−11.7775	+	35.3326i	−0.375264	+	1.12579i
$986$			2.80697i			0.0893923i
$987$		0			0
$988$	14.9491	−	14.9491i	0.475595	−	0.475595i
$989$			35.0333i			1.11400i
$990$	−10.1669	−	3.38896i	−0.323124	−	0.107708i
$991$	−54.1077			−1.71879			−0.859394	−	0.511315i	$-0.829159\pi$
$991$	−54.1077			−1.71879			−0.859394	+	0.511315i	$0.829159\pi$
$992$	0.575324	−	0.575324i	0.0182666	−	0.0182666i
$993$	23.8133	+	23.8133i	0.755691	+	0.755691i
$994$		0			0
$995$	−2.12809	−	4.25617i	−0.0674649	−	0.134930i
$996$	3.55582			0.112670
$997$	23.1318	−	23.1318i	0.732592	−	0.732592i	−0.238541	−	0.971133i	$-0.576669\pi$
$997$	23.1318	−	23.1318i	0.732592	−	0.732592i	0.971133	+	0.238541i	$0.0766690\pi$
$998$	−3.67979	+	3.67979i	−0.116482	+	0.116482i
$999$	8.74219			0.276591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.a.97.2	✓	8
5.3	odd	4		1470.2.m.b.1273.2	yes	8
7.6	odd	2		1470.2.m.b.97.2	yes	8
35.13	even	4	inner	1470.2.m.a.1273.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.a.97.2	✓	8	1.1	even	1	trivial
1470.2.m.a.1273.2	yes	8	35.13	even	4	inner
1470.2.m.b.97.2	yes	8	7.6	odd	2
1470.2.m.b.1273.2	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-0.707107 + 2.12132i) q^{10} +4.79271 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-4.37849 - 4.37849i) q^{13} +(0.707107 - 2.12132i) q^{15} -1.00000 q^{16} +(1.38896 - 1.38896i) q^{17} +(0.707107 - 0.707107i) q^{18} +3.41421 q^{19} +(2.00000 - 1.00000i) q^{20} +(-3.38896 - 3.38896i) q^{22} +(-3.00000 + 3.00000i) q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +6.19212i q^{26} +(-0.707107 + 0.707107i) q^{27} -1.42901i q^{29} +(-2.00000 + 1.00000i) q^{30} -0.813631i q^{31} +(0.707107 + 0.707107i) q^{32} +(3.38896 + 3.38896i) q^{33} -1.96428 q^{34} -1.00000 q^{36} +(-6.18166 - 6.18166i) q^{37} +(-2.41421 - 2.41421i) q^{38} -6.19212i q^{39} +(-2.12132 - 0.707107i) q^{40} -1.92856i q^{41} +(5.83889 - 5.83889i) q^{43} +4.79271i q^{44} +(2.00000 - 1.00000i) q^{45} +4.24264 q^{46} +(6.59588 - 6.59588i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(4.94975 - 0.707107i) q^{50} +1.96428 q^{51} +(4.37849 - 4.37849i) q^{52} +(-7.91376 + 7.91376i) q^{53} +1.00000 q^{54} +(-4.79271 - 9.58541i) q^{55} +(2.41421 + 2.41421i) q^{57} +(-1.01046 + 1.01046i) q^{58} -5.36370 q^{59} +(2.12132 + 0.707107i) q^{60} -9.58541i q^{61} +(-0.575324 + 0.575324i) q^{62} -1.00000i q^{64} +(-4.37849 + 13.1355i) q^{65} -4.79271i q^{66} +(-6.36803 - 6.36803i) q^{67} +(1.38896 + 1.38896i) q^{68} -4.24264 q^{69} +14.9700 q^{71} +(0.707107 + 0.707107i) q^{72} +(-4.81363 - 4.81363i) q^{73} +8.74219i q^{74} +(-4.94975 + 0.707107i) q^{75} +3.41421i q^{76} +(-4.37849 + 4.37849i) q^{78} -1.92856i q^{79} +(1.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(-1.36370 + 1.36370i) q^{82} +(-2.51434 - 2.51434i) q^{83} +(-4.16687 - 1.38896i) q^{85} -8.25744 q^{86} +(1.01046 - 1.01046i) q^{87} +(3.38896 - 3.38896i) q^{88} -9.97908 q^{89} +(-2.12132 - 0.707107i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(0.575324 - 0.575324i) q^{93} -9.32798 q^{94} +(-3.41421 - 6.82843i) q^{95} +1.00000i q^{96} +(11.2275 - 11.2275i) q^{97} +4.79271i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5}+O(q^{10}) \) 8 * q - 8 * q^5	\( 8 q - 8 q^{5} - 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 8 q^{24} - 24 q^{25} - 16 q^{30} + 8 q^{33} - 8 q^{36} + 8 q^{37} - 8 q^{38} + 32 q^{43} + 16 q^{45} - 16 q^{47} + 8 q^{52} - 32 q^{53} + 8 q^{54} + 8 q^{57} - 16 q^{58} - 16 q^{59} - 8 q^{62} - 8 q^{65} - 16 q^{67} - 8 q^{68} + 32 q^{71} - 16 q^{73} - 8 q^{78} + 8 q^{80} - 8 q^{81} + 16 q^{82} + 24 q^{85} - 32 q^{86} + 16 q^{87} + 8 q^{88} - 64 q^{89} - 24 q^{92} + 8 q^{93} - 32 q^{94} - 16 q^{95} - 32 q^{97}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 8 * q^24 - 24 * q^25 - 16 * q^30 + 8 * q^33 - 8 * q^36 + 8 * q^37 - 8 * q^38 + 32 * q^43 + 16 * q^45 - 16 * q^47 + 8 * q^52 - 32 * q^53 + 8 * q^54 + 8 * q^57 - 16 * q^58 - 16 * q^59 - 8 * q^62 - 8 * q^65 - 16 * q^67 - 8 * q^68 + 32 * q^71 - 16 * q^73 - 8 * q^78 + 8 * q^80 - 8 * q^81 + 16 * q^82 + 24 * q^85 - 32 * q^86 + 16 * q^87 + 8 * q^88 - 64 * q^89 - 24 * q^92 + 8 * q^93 - 32 * q^94 - 16 * q^95 - 32 * q^97

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